89/3848–12FE Reference Handbook 10.6 · Statics · p. 95 Moments (Couples): equal, opposite, parallel forces; M = r × F
1. Moment & Equilibrium2. Centroid of a Composite Area3. Coulomb Friction4. Force Resultant5. Rectangle Centroidal Moment of Inertia6. Parallel-Axis Theorem7. Distributed Load Resultant8. Method of Joints9. Two-Force Member10. Ideal Pulley11. Moment of a Force12. Simply Supported Beam Reactions13. Load–Shear–Moment Relations14. Method of Sections (Truss)15. Sagging Cable (Small Sag)16. Overhanging-Beam Reactions17. Radius of Gyration18. Triangle Area Moment of Inertia19. Triangular Distributed Load Resultant20. Three-Force Member21. Couple Moment22. Frames: Multi-Force Members23. Zero-Force Truss Members

Handbook formula

Couple Moment

p. 95 calls a couple two equal, opposite, parallel forces. Its moment is F times the perpendicular spacing and is the same about every point. A single force moved off its line of action is replaced by a parallel force plus the couple M = F d. Collinear equal-and-opposite forces are not a couple.

Force magnitude of each couple arm
Perpendicular spacing

Step-by-step solved example

Replace a 5 kN force 2 m off a point O by a force at O plus a couple.

givenO2 m5 kNequivalent5 kN10 kN·mM = F d = 5 × 25 kN at O + 10 kN·m coupleReplay
A couple is Fd, a free moment vector.

  1. 1. Force at O

    5 kN, same line parallel through O.

  2. 2. Couple

    M=5×2=10 kN·m (sense by right-hand / original rotation).

Answer: 5 kN at O plus 10 kN·m couple

10 practice questions

0/10 correct

1.Moment of a couple about any point is

2.Two couples in a plane add as

3.A couple cannot be reduced to

4.Varignon is about

5.F=80 N, d=0.25 m, M =

6.Equivalent force–couple at a support is how we

7.In 3-D a couple is

8.Equal and opposite collinear forces are

9.Fixed support in 2-D provides

10.Sliding a force along its line of action